{"title":"Numerical Inverse Laplace Transform Using Chebyshev Polynomial ","authors":"Vinod Mishra, Dimple Rani","volume":105,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":591,"pagesEnd":595,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10004329","abstract":"

In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.<\/p>\r\n","references":"\tA. M. Cohen, Numerical Methods for Laplace Transform Inversion, Springer, 2007.\r\n\tR. E. Bellman, H. H. Kagiwada and R. E. Kalba, \u201cNumerical Inversion of Laplace Transforms and Some Inverse Problems in Radiative Transfer,\u201d Journal of Atmospheric Sciences, vol. 23, pp. 555-559, 1966.\r\n\tL. D\u2019Amore, G. Laccetti and A. Murli, \u201cAn Implementation of a Fourier Series Method for the Numerical Inversion of the Laplace Transform,\u201d ACM Transactions on Mathematical Software, vol. 25, No. 3, pp. 279\u2013305, 1999.\r\n\tB. Davies and B. Martin, \u201cNumerical Inversion of Laplace Transform: A Survey and Comparison of Methods,\u201d Journal of Computational Physics, vol. 33, pp. 1-32, 1979.\r\n\tA. Papoulis, \u201cA New Method of Inversion of the Laplace Transform,\u201d Quart. Appl. Math., vol. 14, pp. 405-414, 1956.\r\n\tV. Mishra, \u201cReview of Numerical Inverse of Laplace transforms using Fourier Analysis, Fast Fourier transform and Orthogonal polynomials,\u201d Mathematics in Engineering Science and Aerospace, vol. 5, pp. 239-261, 2014.\r\n\tJ. L. Schiff, The Laplace Transform: Theory and Applications, Springer, 2005.\r\n\tF. A. Uribe, J. L. Naredo, P. Moreno and L. Guardado, \u201cElectromagnetic Transients in Underground Transmission Systems through the Numerical Laplace Transform,\u201d International Journal of Electrical Power and Energy Systems, vol. 24, pp. 215-221, 2002.\r\n\tV. Mishra and D. Rani, \u201cChebyshev Polynomial Based Numerical Inverse Laplace Transform Solutions of Linear Volterra Integral and Integro-differential Equations,\u201d American Research Journal of Mathematics, vol. 1, pp. 22-32, 2015.\r\n\tR. E. Bellman, R.E. Kalaba and J.A. Lockett, Numerical Inversions Laplace Transforms with Applications, American Elsevier Publishing Co., New York, 1966, p. 255.\r\n\tJ. Glyn, Advanced Modern Engineering Mathematics, Pearson Education, 2004 (Indian reprint).\r\n\tH. Sheng, Y. Li and Y. Q. Chen, \u201cApplication of Numerical Inverse Laplace Transform Algorithms in Fractional Calculus,\u201d in Proceedings of FDA\u201910, Article No. 108, pp. 1-6.\r\n\tL. C. Andrews and B. K. Shivamoggi, Integral Transforms for Engineers, PHI, 2003.\r\n\tJ. L. Wu, C. H. Chen and C. F. Chen, \u201cNumerical Inversion of Laplace Transform using Haar Wavelet Operational Matrices,\u201d IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 48, pp. 120-122, 2001.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 105, 2015"}